Spin Chronicles Part 47: Emergence of time I

 It took me a while to gather my thoughts and finally sit down to write about the "emergence of time," as I had promised. But today, the moment felt right—a kairos, as the ancient Greeks might say. And so, here we are.

Let me start with a little detour into history. The ancient Greeks had two words for time: chronos and kairos. While chronos refers to chronological, sequential time—the kind we measure with clocks—kairos is something more elusive. It means "the right or critical moment," a qualitative, almost magical sense of timing. In modern Greek, kairos even extends to mean "weather," hinting at its connection to the unpredictable and the timely.

Kairos emerging from pleroma

As Wikipedia eloquently puts it:

"Kairos has classically been defined as a concept that focused on 'the uniquely timely, the spontaneous, the radically particular.' Ancient Pythagoreans considered kairos one of the most fundamental laws of the universe. It was said to weave together the dualistic nature of existence. Empedocles, the philosopher, linked kairos to the principle of opposites and harmony, making it a cornerstone of conflict and resolution—a concept that even found its way into rhetoric."

Kairos as portrayed in a 16th-century fresco by Francesco Salviati

What is he doing there? Drilling with an electric drill?

But philosophy, as fascinating as it is, often feels like an attempt to impose logical order on a tangled web of ideas. These ideas, of course, spring from our interactions with reality—both conscious and unconscious. For me, though, the real magic lies in mathematical structures that can model both the real and the unreal. And when it comes to making sense of "time," I believe algebra is the key.

It was likely John von Neumann who first pioneered the algebraic approach to quantum theory. His seminal work, Mathematical Foundations of Quantum Mechanics, played a pivotal role in my own intellectual journey. From there, I fell head over heels for the perspectives of Araki, Haag, and Kastler. When I first began studying their works, I had no idea that one day I’d be discussing the intricacies of quantum theory with them in their homes. Most of these conversations were with Rudolf Haag, but it was Daniel Kastler with whom I co-authored three of my papers:

1. A. Jadczyk and D. Kastler, “Graded Lie Cartan Pairs”, Rep. Math. Phys., 25 (1988), 1–51 pdf 
2. A. Jadczyk and D. Kastler, “Graded Lie Cartan Pairs. 2. The Fermionic Differential Calculus”, Ann. Phys., 179 (1987), 169–200 pdf  
   
3. R. Coquereaux, A. Jadczyk, D. Kastler, “Differential and Integral Geometry of Grassmann Algebras”, Rev. Math. Phys., 3 (1991), 63–99 pdf  

These collaborations were a masterclass in honing my abstract algebraic skills—far removed from any immediate real-world applications. At the time, Kastler was deeply invested in promoting the ideas of noncommutative geometry, a field being developed by Alain Connes. Kastler believed this would be the future of physics, and in 1992, he and Thomas Schücker published a paper in the Russian journal Theoretical and Mathematical Physics titled “Remarks on Alain Connes' Approach to the Standard Model in Non-Commutative Geometry,” dedicated to M.C. Polivanov.

Then, in 1994, something remarkable happened. Alain Connes, a mathematician, joined forces with theoretical physicist Carlo Rovelli. Together, they wrote a groundbreaking paper linking noncommutative geometry to the "emergence of time" [1]. This collaboration laid the foundation for a new way of thinking about time—one that transcends the classical, linear view.

Later, Carlo Rovelli, renowned for his work on quantum gravity, distilled these ideas into his popular book The Order of Time [2]. In Part III, titled “The Sources of Time – Quantum Time,” he writes:

"Connes has provided a refined mathematical version of this idea: he has shown that a kind of temporal flow is implicitly defined by the noncommutativity of the physical variables. Due to this noncommutativity, the set of physical variables in a system defines a mathematical structure called a 'noncommutative von Neumann algebra,' and Connes has shown that these structures contain an implicitly defined flow. Surprisingly, there is an extremely close relation between Alain Connes’s flow for quantum systems and the thermal time I have discussed above. Connes has shown that, in a quantum system, the thermal flows determined by different macroscopic states are equivalent, up to certain internal symmetries, and that, together, they form precisely the Connes flow. Put simply: the time determined by macroscopic states and the time determined by quantum noncommutativity are aspects of the same phenomenon."

 

This, I believe, is the essence of what we call "time" in our universe—a variable that doesn’t exist at the fundamental level but emerges from the interplay of quantum and thermal dynamics.

The notes in Rovelli’s book elaborate further:

"[85]. The theorem of Tomita-Takesaki shows that a state on a von Neumann algebra defines a flow (a one-parameter family of modular automorphisms). Connes has shown that the flows defined by different states are equivalent up to internal automorphisms, and therefore define an abstract flow determined only by the noncommutative structure of the algebra.

[86]. The internal automorphisms of the algebra referred to in the above note.

[87]. In a von Neumann algebra, the thermal time of a state is exactly the same as Tomita’s flow! The state is KMS with respect to this flow."

 

On the same subject, M. Heller and W. Sasin published a paper titled Emergence of Time [3]. In Section 6, "Interpretation," they write:

"To define the modular group at, Connes and Rovelli have distinguished the state on A of the form ω(a) = Tr[aω] for every a∈A (which, in the language used by physicists, is a density matrix). Owing to this choice, they were able to argue that the time flow has a statistical (thermodynamic) origin. They emphasize that it is not only the arrow of time that emerges in this way, but also the time flow itself." 

 

Similarly, R. Longo’s paper Emergence of Time states in its abstract:

"We know that a von Neumann algebra is a noncommutative space. About 50 years ago, the Tomita-Takesaki modular theory revealed an intrinsic evolution associated with any given (faithful, normal) state of a von Neumann algebra, so a noncommutative space is intrinsically dynamical. This evolution is characterized by the Kubo-Martin-Schwinger thermal equilibrium condition in quantum statistical mechanics (Haag, Hugenholtz, Winnink), thus modular time is related to temperature. Indeed, positivity of temperature fixes a quantum-thermodynamical arrow of time."

In the following posts, we’ll explore Tomita’s flow of “thermal time” through the lens of a simple geometric Clifford algebra, A ≃ Mat(2,C). We’ll identify A with Mat(2,C) and begin with the concept of a "state," which we’ve already touched on.

References:

[1] A. Connes, C. Rovelli, "Von Neumann algebra automorphisms and time-thermodynamics relation in generally covariant quantum theories", Class. Quantum Grav. 11 (1994) 2899 .

[2] Carlo Rovelli, "The Order of Time", Penguin Books 2018, ISBN 9780735216105.

[3] M. M. Heller and W. Sasin, "Emergence of Time", Phys. Lett. A 250 (1998) 48-54.

[4] R. Longo, "Emergence of Time", Expo. Math. 38 (2020) 240-258.

Life is at the boundary

A Sleepless Odyssey

For over a week, I've barely slept. I've barely eaten. Without my wife, I might not sleep or eat at all. Work has consumed me. My brain spins endlessly, processing algebraic symbols and the elusive objects from Plato's world. Something new is forming. At least, it's new to me.

My brain spins endlessly, processing algebraic symbols and the elusive objects from Plato's world. 

Will it be of use to anyone? Right now, I don't care. It's beautiful, and that's enough. A puzzle is unfolding before me. 

I don't know what the final picture will be. Many pieces are still missing. The box is vast, overflowing with possibilities. Strangely, I find myself returning to ideas from my doctorate. Back then, they were mysteries. Now, I understand them. Now, I develop them.

The Edge of Reality

To satisfy your curiosity, I'll share what I'm working on. Although, I doubt anyone will understand. But I’ll tell you anyway. Think of it as surrealist poetry.

On the edge, there’s a great concentration (critical density) of Black and White...

Our world—our entire reality—is a complex domain. This domain has an edge, and our lives unfold along this boundary. We have no clear view of its interior. Perhaps, just a glimpse. Deep within the domain, a spotlight of consciousness shines, like a lighthouse, illuminating the edge point by point.

A lighthouse, illuminating the edge point by point.

The Cycle of Time

Each point touched by light marks the passage of our "time." Time is cyclical. Reincarnations. For those who live only on the edge, with no insight into the interior, the cycle repeats endlessly. Every point on the edge has its opposite—somewhere, infinitely distant.

Within the domain, time does not flow. Inside, there is no difference between reality and imagination. Inside, Geometry dwells. Geometry akin to Escher’s devils and angels. Our edge is not the only one. There are others, adjacent to ours, with other "lives" existing in different dimensions.

Not only is our "time" cyclical, but our space also loops back on itself. It closes with a cap shaped like a truncated double  light cone.

The Operators of Existence

The domain is filled with operators. Our point on the edge, along with its opposite—the tip of the cap—is also an operator. This operator is anti-commuting with the lighthouse. It remains anti-commuting through all "time." The tangents to the edge are four Dirac gamma operators.

But there is a fifth gamma operator, anti-commuting with the four "normal" ones. Together, they span a five-dimensional space. The domain is "round." But if a "wind" distorts it slightly—it creates unstable gravity waves—that’s GRAVITY.

The Quantum Leap: A Journey Beyond Reality

 The world around us is not merely changing; it is experiencing a quantum leap. This is not a mere evolution but a dramatic transformation, and we are all participants in this grand phenomenon. Some of us are active players, diving headfirst into the unknown, while others are passive witnesses, watching the spectacle unfold. Yet, many continue their daily routines, blissfully unaware of the seismic shifts happening around them.

In my theory of EEQT (Event Enhanced Quantum Theory), these jumps occur at seemingly random, yet precisely timed moments. When the time is ripe, reality takes a leap, and these jumps, theoretically instantaneous, are in truth processes that transcend our material world, touching upon hyper-dimensional realms beyond our comprehension.

The term UFO (Unidentified Flying Object) has evolved into UAP (Unidentified Anomalous Phenomena). These entities are no longer mere flying objects; they are elusive forms that defy our physical understanding. Despite the media's reluctance to embrace the term "hyper-dimensional," the public is gradually being conditioned for the extraordinary revelations that lie ahead.

A flying flock of gees over the pool in Florida?
Or a "form" of a hyper-dimensional origin?

In this rapidly shifting landscape, propelled by the explosion of artificial intelligence, I find myself pondering the union of matter and spirit. Recently, I delved into the works of a kindred spirit, V.V. Varlamov, a professor at the Siberian State Industrial University in Novokuznetsk, Russia. His paper, "On the Union of Matter and Form: Group Theoretical Approach" (Metafizika, 2023), has captivated my mind.

Varlamov begins by exploring the very fabric of our reality: space and time. Are these the fundamental levels of reality, or mere constructs of our perception? He writes:

“Does spacetime make the fundamental level of reality? First, define what are these ‘space’ and ‘time’ comprising the notion of spacetime. Two different frameworks should be distinguished: aprioristic Kantian understanding of space and time as pure forms of our sensibility and the so-called relativistic view on space and time as the forms of existence of matter. Forms of sensibility versus forms of being. Consciousness versus matter. It seems like we are trapped once again within the eternal duality of spirit and matter - nightmare of a philosopher having to choose between the idealistic and materialistic philosophies. As a matter of fact, this duality is only an illusion caused by the mess of words and concepts, as was noted by Bertrand Russel. These two concepts cannot be deduced empirically but precede any experiment making the ground for all the following constructions. According to Kant, space and time are two pure forms of sensory contemplation and principles of a priori knowledge. They are the first and fundamental attributes of our perception, derived from the integrated sensorial experience of human being. Form of contemplation is just an obscure and strongly curved lens mediating our perception of the world. Hence, defining the space and time concepts from experience makes no sense, while defining them by other means yields anything but not space and not time. Here we come to a very important conclusion: space and time are nothing but forms of human conscious contemplation.”

As I read these profound words, I see a reflection of my own thoughts. Varlamov, a mathematician, weaves his contemplations in the language of Real numbers, Quaternions, Spinors, Twistors, and the Conformal Group, even delving into the enigmatic anti-de Sitter space with its two time-like dimensions. He is, in essence, another version of myself, more mathematical in spirit.

In this quantum leap, we are bound not just by the physical world but by a tapestry of consciousness that stretches into the hyper-dimensional. As we stand on the brink of this new reality, we must embrace both the matter and the spirit, understanding that they are not opposing forces but facets of a greater whole. The future is here, and it is beyond anything we have ever imagined.

The Future is Now.

P.S. 24-07-24 13:45 AI at work. My chat with AI today:

Prompt: Can you help me to identify a snake if I give you a photo?

Response: Yes, I'd be happy to help you identify a snake. Please go ahead and upload the photo of the snake.

Prompt: Here it is:

Response: Based on the photo you provided, the snake appears to be a type of garter snake. Garter snakes are non-venomous and common in many parts of North America. They are known for their distinctive pattern, usually consisting of stripes running the length of their bodies.

Here's a bit more detail about garter snakes:

• They often have three stripes running down their bodies, which can be yellow, green, or blue.
• They are usually small to medium-sized snakes, typically ranging from 18 to 26 inches long.
• They are often found near water sources such as ponds, streams, or wetlands, but they can also be seen in gardens and urban areas.

If you need more precise identification or if you have any specific concerns, such as whether the snake is venomous or poses a threat, please let me know!

Prompt: Thanks.

Response: You're welcome! If you have any more questions about snakes or anything else, feel free to ask. Stay safe and have a great day!

But it is NOT a garter snake. As Laura has pointed it to me, it is a semi-aquatic European grass snake. 
https://en.wikipedia.org/wiki/Grass_snake. So, use AI, but do not rely on it when taking decisions. Always double check! If it cam misidentify snakes, it can misidentify missiles as well.

Why? The Purpose of the Universe - Part Five

Laura Knight-Jadczyk

The Cosmological Argument

 

Plato (c. 427–347 BC) and Aristotle (c. 384–322 BC) both posited first cause arguments, though each had certain notable caveats. In The Laws (Book X), Plato posited that all movement in the world and the Cosmos was "imparted motion". This required a "self-originated motion" to set it in motion and to maintain it. In Timaeus, Plato posited a "demiurge" of supreme wisdom and intelligence as the creator of the Cosmos.

Aristotle argued against the idea of a first cause, often confused with the idea of a "prime mover" or "unmoved mover" in his Physics and Metaphysics. Aristotle argued in favor of the idea of several unmoved movers, one powering each celestial sphere, which he believed lived beyond the sphere of the fixed stars, and explained why motion in the universe (which he believed was eternal) had continued for an infinite period of time. Aristotle argued the atomist's assertion of a non-eternal universe would require a first uncaused cause – in his terminology, an efficient first cause – an idea he considered a nonsensical flaw in the reasoning of the atomists.

Like Plato, Aristotle believed in an eternal cosmos with no beginning and no end (which in turn follows Parmenides' famous statement that "nothing comes from nothing"). In what he called "first philosophy" or metaphysics, Aristotle did intend a theological correspondence between the prime mover and a deity; functionally, however, he provided an explanation for the apparent motion of the "fixed stars" (now understood as the daily rotation of the Earth). According to his theses, immaterial unmoved movers are eternal unchangeable beings that constantly think about thinking, but being immaterial, they are incapable of interacting with the cosmos and have no knowledge of what transpires therein. From an "aspiration or desire", the celestial spheres, imitate that purely intellectual activity as best they can, by uniform circular motion. The unmoved movers inspiring the planetary spheres are no different in kind from the prime mover, they merely suffer a dependency of relation to the prime mover. Correspondingly, the motions of the planets are subordinate to the motion inspired by the prime mover in the sphere of fixed stars. Aristotle's natural theology admitted no creation or capriciousness from the immortal pantheon, but maintained a defense against dangerous charges of impiety. (https://en.wikipedia.org/wiki/Cosmological_argument)

~ ~ ~

 In the previous post, I laid out Philip Goff’s ‘Pan-agentialism’ idea which required that he dispense with Schrödinger’s Cat and Many Worlds, resulting in his adoption of Pilot-wave Theory which included ‘rational matter’.

… the stuff of the world is rational stuff.  Even when behaving in a predictable way, its behaviour is the result of a rational impulse, albeit of a very crude kind.  As matter evolves into complex forms, more and more the potential for rational thought and action begins to flower, blossoming in the reflective consciousness of a human being able to discern and respond to practical and theoretical reasons.  This is not just matter changing, but matter maturing, coming to a greater realization of its inherent rational nature.

The pan-agentialist world is, by definition, a world that embodies purpose.  Crucially, however, purpose in this sense does not imply design.  Aristotle did believe in some kind of first cause – an ‘unmoved mover’ – but not a beneficent designer who had crafted the purposes of things.  In Aristotle’s worldview, things just had goal-directed natures, regardless of their origins.  Likewise, if matter, in its fundamental nature, is directed towards reason, then matter has a goal-directed purpose or nature regardless of whether or not it was designed.  It is in this sense that consciousness points to purpose, as an essential component of the best explanation of the emergence of experiential understanding.

Goff proposes that we take pan-agentialism as established (!) and consider it in light of the fine-tuning of physics and, voila! we discover that the two mutually reinforce each other and reinforce the reality of purpose.  And so he declares that the laws of physics are fine-tuned not just for life, but also for the possibility of rational matter achieving a high realization of its nature.  That is, fine-tuning and rational matter need each other; they fit together like a lock and key!

He then launches into a series of Bayesian arguments for Pan-Agentialism. He had previously argued based on the Likelihood Principle, that the fine-tuning of physics for life supports the Value-Selection hypothesis against the Cosmic Fluke Hypothesis.  And now, he uses the same principle saying “the existence of experiential understanding supports pan-agentialism over our standard scientific worldview, as it is much more likely that experiential understanding would have evolved on the former hypothesis than on the latter.”

Goff moves through some cursory discussion about free will that is uninspiring and need not detain us.  He then plunges directly into Theodicy in order to engage with “does God exist?” He points out that there are many examples of horrific suffering in Nature, and that, in fact suffering is built into Natural Selection. He asks “Why would an all-powerful being choose to bring us into existence through such a gruesome, long-winded, tortuous process as a game of ‘survival of the fittest’? … why give us bodies that age, get sick, and fall apart so easily?  Why not instead create immortal, spiritual beings to spend eternity in loving union with God and with each other?”

He then trots out the usual arguments for review, but Goff isn’t having it. He writes:

Personally, I am unconvinced by these proposals.  I agree that there are certain goods we find in the real world – compassion, courage, adventure, scientific enquiry – that would not exist in a more perfect world.  But it seems to me to massively reduce the value of these goods if they were brought about through artificially engineering challenges and difficulties.

Did Goff forget that he just argued for “matter maturing, coming to a greater realization of its inherent rational nature” and did he not note that horrific suffering was part and parcel of Natural Selection?

Of course, Goff has set the argument up to be a Straw Man – an omnipotent, omniscient god who created the world via fiat – and who is immoral, in Goff’s opinion, for deliberately creating a world such as ours. But he slogs on toward the Cosmological argument: without a creator God, we have no explanation for why the universe came to be nor any explanation for anything at all.  He notes the atheist response: why does the universe require an explanation, but God gets a free pass?

·       The Kālam Cosmological Argument:  The crucial difference between God and the universe is that the universe began to exist whereas God did not.  Things that begin to exist require causal explanation, whereas things that are timeless, do not.  See: Kalām cosmological argument https://en.wikipedia.org/wiki/Cosmological_argument

·       The Contingency Argument:  the reason the universe cries out for explanation is that it is contingent, which means that it might not have existed. If something exists but might not have existed, then we need to give some explanation as to why it does exist.  God, in contrast, is not contingent; God is a necessary being, a being that has to exist. See Aquinas Argument from contingency: https://en.wikipedia.org/wiki/Cosmological_argument

Goff tells us that Cosmological arguments proceed in two stages.  First, the argument tries to establish that a timeless/necessary being has to exist to complete the Great Chain of Explanation.  Second, the arguments try to show that this timeless/necessary being must have the characteristics of the Omni-God: omniscient, omnipotent, and perfectly good.  Goff then makes an eminently rational remark: “If we are rationally compelled to accept the existence of a timeless, necessarily existent entity, why not suppose that the entity is the universe itself, rather than postulating something supernatural outside of the universe?” Good idea, in my opinion. He then says something more: “… at best, these arguments prove that the universe’s existence as a spatiotemporal entity is contingent and began at a finite point in the past.  A possibility rarely considered in these discussions is that the universe, prior to the Big Bang, existed in a non-spatiotemporal form.  … once we have committed to the existence of a necessary and timeless foundation of existence, we face a choice between two theoretical possibilities:

Option 1: The necessary and timeless foundation of existence is distinct from the universe and brought the universe into being.

Option 2: The necessary and timeless foundation of existence became the universe a finite period of time ago, undergoing a radical change analogous – although obviously more extreme – to a caterpillar becoming a butterfly.

That is, the basic cosmological argument of either type merely establishes that a first cause exists, not that it has the attributes of a theistic god, such as omniscience, omnipotence, and omnibenevolence. 

However, some cosmologists and physicists argue that a major challenge to the cosmological argument is the nature of time:  The Big Bang theory states that it (the Big Bang) is the start of both space and time. The claim of the cosmologists and physicists is that the question "What was there before the Universe?" becomes meaningless when considering a situation without time. Some even say that asking what occurred before the Big Bang is like asking what is north of the North Pole?  (Gott III, J. Richard; Gunn, James E.; Schramm, David N.; Tinsley, Beatrice M. (March 1976). "Will the Universe Expand Forever?" Scientific American. p. 65. https://www.jstor.org/stable/24950306).

Getting back to Goff.  He notes that Ockham’s razor enters and eliminates option 1 since option 2 postulates fewer entities. Fine. Goff then brings to our notice the ideas of Joshua Rasmussen who argues that “the Ultimate Foundation of all reality cannot involve arbitrary limits.  … The Ultimate Foundation, by definition, must leave nothing to be explained.  The Ultimate Foundation cannot have a certain amount of power, knowledge, and goodness, whilst not being all-powerful, all-knowing, and perfectly good.  For it would then cry out for explanation why the Ultimate Foundation has precisely that level of power (and not more or less), that level of knowledge, and that level of goodness – and these explanatory demands would undermine its putative status to be the point where explanations come to an end.”

Goff agrees.  Arbitrary limits demand explanations. He then says: “We would still want to know why that maximally perfect exists rather than the even simpler hypothesis of nothing at all existing… And the Omni-God hypothesis, even if it is very simple, is not compatible with the data of evil and suffering.  …Those who deny cosmic purpose cannot explain cosmological fine-tuning, believers in the Omni-God cannot explain the evil and suffering we find in the world.”

Goff next engages with Theists, sceptical theists, etc. He allows that the sceptical theists’ way of defusing the problem of evil is at least somewhat effective: “If God did have a reason for allowing suffering, would I likely know about it?”  And the answer is “no” because the cognitive gap between humans and God is so vast that there is no comparison, no way humans could understand any such reasons.  But then, Goff diverts to his own idea: the ‘Cosmic Sin Intuition.’  That is, “it would be immoral for an all-powerful being to deliberately create a universe like ours.” He writes:

I cannot rule out that there might be all sorts of goods and evils I have no clue about, and maybe if I took them into account, the Cosmic Sin Intuition would lose its force.  But we do have substantial knowledge of morality, and no reason to think that this knowledge isn’t up to the task of assessing the Cosmic Sin Intuition.

Following a few desultory feints, he then concludes that the only rational position to take is to conclude that the Omni-God does not exist and that “we have very good reason to accept the Cosmic Sin Intuition.  And the Cosmic Sin Intuition entails that the Omni-God does not exist.” His case is as follows:

The standard line in the philosophical literature goes as follows:

In the old days, atheist philosophers tried to demonstrate that God’s existence is logically incompatible with the existence of evil and suffering, and hence that, given evil and suffering exist, God’s non-existence can be logically demonstrated.  This approach is known as the logical version of the argument from evil.

Nowadays, most philosophers on both sides of the debate accept that the logical version of the argument is too strong.  Even if we can’t think of any good reasons why God might have allowed suffering, we can’t logically demonstrate that there are no such reasons.  Thus, contemporary atheists tend to argue not that evil and suffering logically entail God’s non-existence, but rather that they are good evidence for God’s non-existence. 

·       The Cosmic Sin Intuition.  It would be immoral for an all-powerful being to deliberately create a universe like ours.

·       Therefore, if our universe has a creator, She (sic) is either not all-powerful or not perfectly moral (or both).

·       Therefore, there is no such thing as the Omni-God.

By defending the inherent plausibility of the Cosmic Sin Intuition, we can build a very strong – although not logically certain – case against the existence of the Omni-God, one which avoids the sceptical theist critique.

Goff then announces that he is going to propose “Cosmic Purpose Without God.”  That will be the next post. But before I end this one, I’d like to just mention that there is an old solution to the problems that Goff and so many others appear to be struggling with, and not very successfully in my view: the ‘Unity of Being’ theory of 13th century Andalusian mystic and philosopher Muhyiddin Ibn Arabi.  But, I will come to that eventually.

Poet in a Garden, by Ali of Gloconda, c.1610-15, via Wikimedia.

The Physics of Densities and the Problem of Time

We communicate using words. Some of our words (though not all) carry meanings. We communicate our thoughts, idea, emotions. There are different levels of communication. The meaning of the word can be found in a dictionary or a thesaurus. But words put together into sentences, and sentences into blocks may carry meaning that are not in a dictionary. The "whole" is more than the sum of its parts. We know it from our experiences. But we also know from our experience that the communication can go deeper when we also listen to the pauses between words. Thus listening adds extra dimension to the reading experience alone. And when we see the body language, when we do feel the physical presence of the person, it adds even more dimensions.

But what exactly are thoughts? And what exactly is "communication?"

In 2006 two physicists, Elisabeth Rausher

and Russell Targ, 

published a paper in Proceedings of the conference of American Institute of Physics under the title  "Investigation of a Complex Space-Time Metric to Describe Precognition of the Future" [1]. In the original 2001 version of the paper [1a]  (still available here) the title was expanded by adding at the very beginning "The Speed of Thoughts:" - though the abstract of the paper was exactly the same.

Let me quote from the Introduction ofv this paper:

" (...) Now in the twenty-first century, the evidence has become overwhelming that our thoughts and bodies can be directly affected and influenced by the thoughts of another person or by events and activities at a distant location blocked from ordinary perception. (...)"

It is somewhat surprising that the American Institute of Physics, a serious institution,  allowed for a publication of such a statement. And "Precognition of the Future"? Is it not considered as pseudo-science? Or, in  the best case, as "fringe science"? Strange. I leave the Reader speculation about possible causes of such a "faux pas".

But let us return to the subject of thoughts and thinking. What is this THINKING? When I am thinking about thinking a handy phrase comes to my mind: Thinking is information processing". Happy? I m not in the least. Because what is "information" and what is "processing"? I am thinking (without processing) that perhaps it should be the other way around. Perhaps thoughts are primary, and information is a concept that has been abstracted by thinking from the data and put into a linear order of mathematical abstraction by organized thoughts of mathematicians? 

We notice that the paper by Rauscher and Targ has been published in a volume entitled "CP863, Frontiers of Time, Retrocausation—Experiment and Theory, edited by D. P. Sheehan". We see the term "Frontiers of Time". How time is related to thinking?  And what is the algebra of thinking and time? Because some math is certainly necessary, sooner or later. But which math? Logic? Topology? My answer is : algebra. Logic can be described in terms of algebra (Boolean algebra, matrices, commutative and non-commutative), and topology is a later concept, there would be no topology without algebra (homotopy groups, homology, Chern classes etc.)

Algebra? But which kind of algebra? The simplest one is probably the algebra of 2x2 complex matrices. It is good for toy models. But to describe states of pure awareness (densities) and transitions between them, we need infinite dimensional algebra. In mathematics we are being taught about Clifford algebras, and more general C* algebras. We also come across a strange structure of the "Calkin algebra". This is related to "phase transitions", and we will be interested in such transitions, except that for a popular in mathematical solid state physics "Ising model", as it is mathematically analyzed in [3]. But all this will come later. For now we will have to discuss the problem of thoughts, thinking, states of awareness, and, last but not least, time.

Mathematicians "classify" their structures, much like "taxonomy" in biology. These structures come into families, but there are also "exotic" structures. Physicists find many different applications for standard mathematical structures, within families, but what about those singular exotic structures. One such exotic structure is "octonions" and related "exceptional Jordan algebra", the algebra of 3x3 matrices over octonions. Physicists have their own exotic structures. One such structure is an elusive "magnetic monopole" (see [4]). What can be an application of such exotic structures? Elementary particle physics? That would be not exotic at all. Exotic structures are to be applied to exotic problems. The problem of consciousness and of time - is such a problem. But the problem of consciousness and the problem of time needs an infinite number of dimensions. How infinite? There is a hierarchy of infinities. Countable infinity is not sufficient.

Concerning "dimensions: The monograph [4] is devoted entirely to the problem of "time". It also talks about "topology" and "quantization of shapes" - rather advanced mathematics is required here. Then we find this piece:

"I  had  the  fortune  of  having  as  a  brother-in-law  one  of  the  greatest mathematicians of recent times, Bill Thurston. Bill and I lived a few blocks from each other in Berkeley, and we had many conversations about  careers  (as  a  graduate  student,  he  was  convinced  that  he would  never  find  a  good  job),  mathematics,  and  physics.  He  was fascinated with my description of what we knew about the universe. He asked me if anybody had seriously considered a multiconnected universe?  Did  he  mean  wormholes,  passageways  that  potentially connected  one  part  of  the  universe  with  another?  No,  he  had something far simpler and much more elegant in mind. Bill  was  ultimately  most  famous  for  his  advances  in  topology, complex  geometries  that  went  far  beyond  our  normal  imagination. He told me that he had actually mastered the skill of being able to think in four dimensions. Few people believed him, until he produced a  vast  array  of  wonderful  theorems  that  he  claimed  he  had discovered by simply looking at surfaces in 4D space in his mind. It turns out, oddly, that math problems in three and fewer dimensions are relatively easy, and problems in five or more dimensions are also relatively  easy,  but  dealing  with  four  dimensions  is  very  tough. Thanks  to  his  work  in  four  dimensions,  Bill  was  to  win  the  FieldsMedal, the “Nobel Prize of mathematics,” before he turned forty.

And yet, surprisingly, the author avoids the subject of Kaluza-Klein theories and our reality having more than three space and one time dimension. In this respect Rauscher and Targ go deeper, and beyond main stream physics, as they allow for a complex 8-dimensional spacetime with acausal connections. 

How do we go from a finite number of dimension to infinite number? Nowadays we know the answer - by "quantization". We quantize a mechanical system by considering the space of functions (waves) on the configuration space. We call it "first quantization". In this first quantization the number of degrees of freedom of the system is finite and sharp. But then we consider functions on the space of functions, we "second quantize" the system, and even the number of particles becomes "wavy". We can thus proceed to the third and fourth quantization etc., though no one has an idea where to end and why?

From quantum theory, so successful for not quite well understood reasons, new insights came. Richard Feynman developed a technique called "integral over trajectories". Every classical trajectory acquires a complex "amplitude", whose modulus squared can be interpreted as a "probability". Then "real" trajectories of Newtonian physics are simply those "most probable ones" ("extremal"). Yet all those other trajectories are also important if we want to make quantum theoretical calculation agree with the observed, sometimes strange indeed, reality. Somehow, it would seem, our consciousness, whatever reality is hiding behind this concept, makes the "most probable" "real". The naïve reality of tables and chairs is just the most probable effect of the process of actualization of quantum probability waves.  Or so it seems. The very process of this actualization is still an enigma known as "the quantum measurement problem".

Quantum theory, in fact, is about measurements. The fundamental uncertainty relations as well as the more general concept of complementarity deal with restrictions on measurements. When measuring the momentum we disturb the position, when measuring the postion, we disturb the momentum. Measuring position forces the quantum object to behave like a particle. Measuring its momentum we force the object exhibit its wave-like properties. Yet the very process of measurement, its dynamics, is still a puzzle - it escapes the theoretical description. The idea that there is no measurement problem and no "quantum jumps", that the quantum wave function is a "hidden variable" that somehow, for some reasons "pilots" the classical particle is attractive, but does not explain where the mysterious quantum force that tells the particle to wander in space against the standard laws of mechanics is incomplete and has limited applications. 

Another approach to the measurement problem has other attractive properties and other limitations [5]. It is an old story that "consciousness" is somehow involved automatically in quantum theory. As John Archibald Wheeler termed it "No phenomenon is a phenomenon unless and until it is an observed phenomenon". But then we need to explain "consciousness" and "observation". Wheeler then continued:

" no elementary quantum phenomenon is a phenomenon until, in Bohr's words [10], "It has been brought to a close" by  "an irreversible act of amplification."  What we call the past is built  on bits. (...)  

"Consciousness".  We have traveled what may seem a dizzying path. First,  elementary  quantum  phenomenon brought  to  a  close by an  irreversible act of  amplification.  Second,  the  resulting information expressed in  the  form  of bits.

Third,  this  information used by observer-participants — via communication — to establish  meaning.  Fourth, from  the past  through the  billeniums to  come, so many observer-participants,  so many bits,  so much exchange of information, as to  build what  we call existence. Doesn't  this  it-from-bit  view of existence seek to  elucidate  the  physical world, about  which we know something, in terms of an entity about  which we know almost nothing,  consciousness  [134-137]? "

And then:

"Six:  Capitalize  on  the  findings  and  outlooks  of information theory  [160-163], algorithmic  entropy  [164],  evolution  of organisms  [165-167]  and  pattern  recogni-tion  [168-175].  Search out  every link each has with  physics  at  the  quantum level. Consider, for instance,  the  string  of bits 1111111 . . .  and its representation as the sum of the  two strings 1001110...  and 0110001...  Explore  and exploit the  connection  between  this  information-theoretic statement  and  the findings of theory  and experiment on the correlation between the polarizations of the two photons  emitted in the  annihilation of singlet positronium  [176] and in like Einstein-Podolsky-Rosen experiments  [177],  Seek out, moreover, every realization  in the  realm of physics of the information-theoretic  triangle inequality recently discovered by  Zurek  [178]. Finally:  Deplore?  No,  celebrate  the  absence  of a  clean  clear  definition  of  the term  "bit"  as  elementary  unit  in  the  establishment  of meaning.  We reject  "that view  of science  which  used  to  say,  'Define  your  terms  before  you proceed.'  The truly  creative  nature  of any forward  step in human knowledge," we know,  "is such that theory, concept, law and method of measurement — forever inseparable — are born into the  world in union  [179]."  If and when we learn  how to  combine bits  in fantastically  large  numbers to  obtain  what  we call  existence,  we will know better what we mean  both  by bit  and by existence. A  single question  animates  this  report:  Can  we ever expect  to  understand  existence?  Clues  we have,  and  work to  do, to  make headway on that  issue.  Surely someday,  we  can  believe,  we will  grasp  the  central  idea  of it  all  as  so simple,  so beautiful,  so compelling that we will all say to each other,  "Oh, how -could it  have been otherwise!  How could we all have been so blind so long!" 

If "it" comes from "bit", which sounds true, if matter is actualized and organized information, if there are organization levels that we may call "densities" - then, contrary what Wheeler suggests [6], we must not celebrate the fact that we do not have a clear definition of "bit", that we talk about information without being able to define it. This job needs to be done, and it will.

References:

[1] Elizabeth A. Rauscher and Russell Targ, "Investigation of a Complex Space-Time Metric to Describe Precognition of the Future",  AIP Conference Proc. 863 (2006),  http://dx.doi.org/10.1063/1.2388752

[1a]Elizabeth A. Rauscher and Russell Targ,  "The Speed of Thought: Investigation of a Complex Space-Time Metric to Describe Psychic Phenomena", Journal of Scientific Exploration", Vol. 15, No. 3, pp. 331–354, 2001 0892-3310/01, DOI:10.1063/1.2388752

[2] A. L. Carey, "Algebras  Almost  Commuting  with Clifford  Algebras", JOURNAL  OF  FUNCTIONAL  ANALYSIS  88,  279-298  (1990) 

[3] R. A. Sventkovsky, "The Equations of Dirac and Maxwell as a Result of Combining Minkowski Space and the Space of Orientations into Seven-Dimensional Space-Time",     October 2020 Mathematical Notes 108(3-4):381-393, DOI: 10.1134/S0001434620090072

[4] Edward Anderson, "The Problem of Time: Quantum Mechanics Versus General Relativity", Springer International Publishing, Oct 3, 2017 - Science - 920 pages

(...) This book shows moreover that eight of the nine facets of the Problem of Time already occur upon entertaining background independence in classical (rather than quantum) physics.(...) This book explains how, none the less, a local resolution of the Problem of Time can be arrived at after various reconceptualizations of the facets and reformulations of their mathematical implementation.  Self-contained appendices on mathematical methods for basic and foundational quantum gravity are included. Finally, this book outlines how supergravity is refreshingly different from GR as a realization of background independence, and what background independence entails at the topological level and beyond.

[5] Henry P. Stapp "Mindful Universe Quantum Mechanics and the Participating Observer", The Frontiers Collection, Springer, 2011, ISBN: 9783642180750,9783642180767,3642180752,3642180760, 
The classical mechanistic idea of nature that prevailed in science during the eighteenth and nineteenth centuries was an essentially mindless conception: the physically described aspects of nature were asserted to be completely determined by prior physically described aspects alone, with our conscious experiences entering only passively. During the twentieth century the classical concepts were found to be inadequate. In the new theory, quantum mechanics, our conscious experiences enter into the dynamics in specified ways not fixed by the physically described aspects alone. Consequences of this radical change in our understanding of the connection between mind and brain are described. This second edition contains two new chapters investigating the role of quantum phenomena in the problem of free will and in the placebo effect.

[5] John Archibald Wheeler, "Information, Physics, Quantum: the Search for Links".

This  report  reviews what  quantum  physics  and information theory  have to  tell  us about  the  age-old  question,  How come  existence?  No escape is evident  from  four conclusions:  (1) The world cannot  be a giant  machine, ruled by any  preestablished continuum  physical  law.  (2)  There  is  no  such  thing  at  the  microscopic level  as space  or  time  or  spacetime  continuum.  (3) The  familiar  probability  function  or functional,  and  wave equation  or  functional wave equation, of standard  quantum theory  provide  mere  continuum  idealizations  and  by  reason  of this  circumstance conceal the  information-theoretic  source from  which they  derive. (4) No element  in the  description  of physics shows  itself  as closer  to  primordial than  the  elementary quantum phenomenon, that is, the  elementary  device-intermediated act of posing a yes-no physical question and  eliciting  an  answer or, in brief,  the  elementary  act of observer-participancy.  Otherwise stated,  every  physical  quantity,  every it,  derives its ultimate  significance from  bits, binary yes-or-no indications, a conclusion which

we epitomize in the  phrase,  it from  bit.

P.S. Here is a piece from the discussion with "us in the future"